Topic 4: Special Relativity - Lorentz transformations

[Ghideon]

55 minutes ago, Jan Slowak said:

Yes, or a No, but then you have to counter-argument.

And

1 hour ago, Jan Slowak said:

This is no answer. If you answer NO, you must counter-argument.

I’ll try to figure out what kind of answer you could be looking for that is compatible with the above statements. 

[beecee]

1 hour ago, Ghideon said:

And

I’ll try to figure out what kind of answer you could be looking for that is compatible with the above statements. 

I really admire your persistence and courage against such arrogance and ignorance.

[Jan Slowak]

18 hours ago, Ghideon said:

And

I’ll try to figure out what kind of answer you could be looking for that is compatible with the above statements. 

Another explanation for the same phenomenon. A reference system S' moves on the x-axis to the right at a constant speed v > 0.
When S' passes the point P₀, its clock is reset, t' = 0. At the same time, an event, a light signal, occurs in the point P_x. P_x is at a distance x from the point P₀.

While the light signal moves towards S', S' moves to the right. When the light signal reaches S', two distances occur on the x-axis. Distance [P₀, S'] and distance [S', P_x].

The length of these two distances is:
Distance [P₀, S'] = vt'
Distance [S', P_x] = ct'
Then we have the following relationship: x = vt'+ ct'.

Is this right?

 

 

 

[swansont]

52 minutes ago, Jan Slowak said:

Another explanation for the same phenomenon. A reference system S' moves on the x-axis to the right at a constant speed v > 0.
When S' passes the point P₀, its clock is reset, t' = 0. At the same time, an event, a light signal, occurs in the point P_x. P_x is at a distance x from the point P₀.

You have a similar problem to one Ghideon already pointed out.

This is the S' frame, yet you are saying it's a distance x. S' should be using primed coordinates.

 

I also don't see the point of making the problem more complicated.

[Jan Slowak]

17 minutes ago, swansont said:

You have a similar problem to one Ghideon already pointed out.

This is the S' frame, yet you are saying it's a distance x. S' should be using primed coordinates.

 

I also don't see the point of making the problem more complicated.

It is not a similar problem, but it is exactly the same problem with clearer explanations and pictures. I was going to help Ghideon move on. 
The sum of the two lengths for S' is vt' + ct' and it is the same length as x in S. 

We have two reference systems but we have only one reality!

 

[swansont]

34 minutes ago, Jan Slowak said:

It is not a similar problem, but it is exactly the same problem with clearer explanations and pictures. 

Yes, mixing the frames in your setup is the exact problem Gideon pointed out. 

It is incorrect using S' to refer to a distance between those points as x. Incorrect statements make nothing clearer.

 

 

next issue: you say "At the same time, an event, a light signal, occurs in the point P_x "

At the same time in whose frame?

 

(I have to note that both of these issues have come up previously in these discussions. I'm not saying anything that hasn't already been pointed out. We will get nowhere if you persist in making the same omissions or errors)

[Strange]

48 minutes ago, Jan Slowak said:

We have two reference systems but we have only one reality!

What does "one reality" mean? We know different observers will measure different quantities (energy, length, time, ordering of events, etc.).

There are very few things that are invariant between observers and which could therefore be described as "one reality". 

[Ghideon]

3 hours ago, Jan Slowak said:

Another explanation for the same phenomenon. A reference system S' moves on the x-axis to the right at a constant speed v > 0.
When S' passes the point P₀, its clock is reset, t' = 0. At the same time, an event, a light signal, occurs in the point P_x. P_x is at a distance x from the point P₀.

While the light signal moves towards S', S' moves to the right. When the light signal reaches S', two distances occur on the x-axis. Distance [P₀, S'] and distance [S', P_x].

The length of these two distances is:
Distance [P₀, S'] = vt'
Distance [S', P_x] = ct'
Then we have the following relationship: x = vt'+ ct'.

Is this right?

 

No, it is not right.

2 hours ago, Jan Slowak said:

It is not a similar problem, but it is exactly the same problem with clearer explanations and pictures. I was going to help Ghideon move on. 
The sum of the two lengths for S' is vt' + ct' and it is the same length as x in S. 

No, it is not right.

On 6/20/2019 at 5:50 PM, Jan Slowak said:

I analyze and talk about the derivation of LT. We don't have them yet! You cannot use them as counter-arguments.

That is not an excuse for using invalid statements about relativity. Lack of rigour regarding the frames of reference can and will lead to contradictions regarding the math of Special Relativity. Personally I am not moving on without addressing that properly: Some readers might interpret such contradictions as problems with the theory of relativity itself* rather than issues with the descriptions and examples in this thread. That would be unfortunate, especially in the mainstream section of the forum.

If multiple frames of reference are used the only way I know of, that gives correct results within Special Relativity, is to use Lorentz Transform or derive Lorentz Transform to be able to move between the frames of reference. So let's try another approach: Even if we are not allowed to use Lorentz Transform for argumentation yet we still have Einstein's postulates, and simply adding distances in one frame of reference to get a distance in another frame of reference is not compatible with Einstein's postulates.

Question: what postulates are we going to use? Can we for instance state that the speed of light is invariant? Are we starting from other postulates?

 

 

 

 

On 6/20/2019 at 5:50 PM, Jan Slowak said:

Please, do not send other pictures.

[swansont]

1 hour ago, Strange said:

What does "one reality" mean? We know different observers will measure different quantities (energy, length, time, ordering of events, etc.).

There are very few things that are invariant between observers and which could therefore be described as "one reality". 

To add to this: we can agree that an event happened. It can't happen in some frames but not others. What we can't do is agree on when and where, and sometimes even the order of multiple events will not be agreed upon.

[Jan Slowak]

On 6/21/2019 at 4:37 PM, swansont said:

Yes, mixing the frames in your setup is the exact problem Gideon pointed out. 

It is incorrect using S' to refer to a distance between those points as x. Incorrect statements make nothing clearer.

  

 

next issue: you say "At the same time, an event, a light signal, occurs in the point P_x "

At the same time in whose frame?

 

(I have to note that both of these issues have come up previously in these discussions. I'm not saying anything that hasn't already been pointed out. We will get nowhere if you persist in making the same omissions or errors)

I do not mix with reference systems. I use them in the same way as in

[3] The special and general theory of relativity; Albert Einstein; The first part; About the special theory of relativity; 2006; swedish
[7] Modern Physics; Second edition; Randy Harris; Chapter 2; Special Relativity; 2008

You make measurements in a reference system and equate the result with the variable from the other.
For example: x = Ax' + Bt'; LTx': x' = (x – vt)γ; LTt': t' = (t – vx/c²)γ

What is the problem? Where are the errors I make in the pictures Fig. 4-06, Fig. 4-07 and how I describe the phenomenon?

On 6/21/2019 at 5:00 PM, Strange said:

What does "one reality" mean? We know different observers will measure different quantities (energy, length, time, ordering of events, etc.).

There are very few things that are invariant between observers and which could therefore be described as "one reality". 

We have only one reality, but each of the observers expresses and describes their measurements with their own variables.
We have an event somewhere on the x-axis of S.
S denotes the event with E = (x, t).
S' denotes the event with E' = (x', t').
But for both reference systems, it's all about one and the same event!
What is the problem with this?

On 6/21/2019 at 6:25 PM, Ghideon said:

No, it is not right.

No, it is not right.

That is not an excuse for using invalid statements about relativity. Lack of rigour regarding the frames of reference can and will lead to contradictions regarding the math of Special Relativity. Personally I am not moving on without addressing that properly: Some readers might interpret such contradictions as problems with the theory of relativity itself* rather than issues with the descriptions and examples in this thread. That would be unfortunate, especially in the mainstream section of the forum.

If multiple frames of reference are used the only way I know of, that gives correct results within Special Relativity, is to use Lorentz Transform or derive Lorentz Transform to be able to move between the frames of reference. So let's try another approach: Even if we are not allowed to use Lorentz Transform for argumentation yet we still have Einstein's postulates, and simply adding distances in one frame of reference to get a distance in another frame of reference is not compatible with Einstein's postulates.

Question: what postulates are we going to use? Can we for instance state that the speed of light is invariant? Are we starting from other postulates?

 

 

 

 

I ask you the same question that I asked to swansont. Where are the errors I make in the pictures Fig. 4-06, Fig. 4-07 and how I describe the phenomenon?
Be specific, please.

[Ghideon]

45 minutes ago, Jan Slowak said:

I ask you the same question that I asked to swansont. Where are the errors I make in the pictures Fig. 4-06, Fig. 4-07 and how I describe the phenomenon?
Be specific, please.

What postulates am I allowed to use?

[Strange]

52 minutes ago, Jan Slowak said:

We have only one reality, but each of the observers expresses and describes their measurements with their own variables.
We have an event somewhere on the x-axis of S.
S denotes the event with E = (x, t).
S' denotes the event with E' = (x', t').
But for both reference systems, it's all about one and the same event!
What is the problem with this?

I'm not sure. So far the only problem is your misuse of mathematics (mixing frames, swapping frames, etc.)

53 minutes ago, Jan Slowak said:

I do not mix with reference systems.

Denying it doesn't stop it being true.

[swansont]

2 hours ago, Jan Slowak said:

I do not mix with reference systems. I use them in the same way as in

[3] The special and general theory of relativity; Albert Einstein; The first part; About the special theory of relativity; 2006; swedish
[7] Modern Physics; Second edition; Randy Harris; Chapter 2; Special Relativity; 2008

You make measurements in a reference system and equate the result with the variable from the other.
For example: x = Ax' + Bt'; LTx': x' = (x – vt)γ; LTt': t' = (t – vx/c²)γ

What is the problem? Where are the errors I make in the pictures Fig. 4-06, Fig. 4-07 and how I describe the phenomenon?

 

You didn’t answer my question. You say two things happen at the same time. I asked in what frame. 

[Jan Slowak]

15 hours ago, swansont said:

 

You didn’t answer my question. You say two things happen at the same time. I asked in what frame. 

Fig. 4-06, Fig. 4-07:
When S' in its motion is in the S-origo, when t = t' = 0, then the event in S arises at a distance x from the S-origo.

17 hours ago, Ghideon said:

What postulates am I allowed to use?

You can use the same postulates used in the literature:

[3] The special and general theory of relativity; Albert Einstein; The first part; About the special theory of relativity; 2006; swedish
[7] Modern Physics; Second edition; Randy Harris; Chapter 2; Special Relativity; 2008

 

17 hours ago, Strange said:

I'm not sure. So far the only problem is your misuse of mathematics (mixing frames, swapping frames, etc.)

Denying it doesn't stop it being true.

Fig. 4-06, Fig. 4-07:
Can you be more specific and write what are the errors I do?
Please check my answers to Ghideon and swansont.

[Strange]

18 minutes ago, Jan Slowak said:

Can you be more specific and write what are the errors I do?

No point. You will just ignore them again.

(If you really want to know, just read back through all your threads and don't just dismiss all the replies as being wrong because they disagree with you. Actually think about what is said, and maybe you will be able to discover your errors. But you aren't interested, so I am not interested in repeating the same explanations.)

[Ghideon]

1 hour ago, Jan Slowak said:

You can use the same postulates used in the literature:

 [3] The special and general theory of relativity; Albert Einstein; The first part; About the special theory of relativity; 2006; swedish
[7] Modern Physics; Second edition; Randy Harris; Chapter 2; Special Relativity; 2008

Post the postulates here please.

[swansont]

2 hours ago, Jan Slowak said:

Fig. 4-06, Fig. 4-07:
When S' in its motion is in the S-origo, when t = t' = 0, then the event in S arises at a distance x from the S-origo.

 

Figs 4-06 and 4-07 are labeled with S' , implying that you are using the S' frame. This passage implies the distance is in the S frame. This a contradiction and calls into question your claim that you aren't mixing frames.

And I already called your attention to this confusion.

I have to say that when you quote passages instead of directly answering it gives the indication that you really don't know what you're talking about, and are hoping the quote addresses the question. Also, barging forward without addressing or correcting mistakes is not helpful. To echo what Strange said — why should we bother to answer if we will be ignored? Why should this thread stay open?

 

 

 

[Jan Slowak]

4 hours ago, Ghideon said:

Post the postulates here please.

From Wikipedia:
1) The special theory of relativity postulates that the speed of light in vacuum is constant equal to c for all observers in uniform relative motion.
2) All systems, where observers move at a constant speed, inertial systems, are equivalent and therefore the laws of physics must give the same results for all of them.

4 hours ago, swansont said:

 

Figs 4-06 and 4-07 are labeled with S' , implying that you are using the S' frame. This passage implies the distance is in the S frame. This a contradiction and calls into question your claim that you aren't mixing frames.

And I already called your attention to this confusion.

I have to say that when you quote passages instead of directly answering it gives the indication that you really don't know what you're talking about, and are hoping the quote addresses the question. Also, barging forward without addressing or correcting mistakes is not helpful. To echo what Strange said — why should we bother to answer if we will be ignored? Why should this thread stay open?

  

 

 

I didn't want to complicate pictures unnecessarily. But in my description of Figs. 4-06 and 4-07 one could read what applies to S' and what applies to S.
I attach copies of these two pictures where I draw S in the point P₀.

[swansont]

2 hours ago, Jan Slowak said:

 

I didn't want to complicate pictures unnecessarily. But in my description of Figs. 4-06 and 4-07 one could read what applies to S' and what applies to S.
I attach copies of these two pictures where I draw S in the point P₀.

You could also answer the question.

[Ghideon]

 

8 hours ago, Jan Slowak said:

Fig. 4-06, Fig. 4-07:
Can you be more specific and write what are the errors I do?

Ok: failure to be specific regarding frames of reference S and S’ makes this specific statement 

On 6/21/2019 at 1:56 PM, Jan Slowak said:

we have the following relationship: x = vt'+ ct'.

incompatible with the first postulate

2 hours ago, Jan Slowak said:

The special theory of relativity postulates that the speed of light in vacuum is constant equal to c for all observers in uniform relative motion

[Ghideon]

Or in other words: using time t’ from the primed coordinates to calculate a distance  x in the unprimed coordinate system assumes Newtonian physics and Galilean transformations. 

[Jan Slowak]

11 hours ago, swansont said:

You could also answer the question.

If you mean your question At the same time in whose frame? then my answer is as follows: in S, this should be obvious.
I write in my explanation of the picture Fig. 4-05: At the same time, an event, a light signal, occurs in the point P_x.
P_x is in the reference system S (x refers to S, x' refers to S').

 

10 hours ago, Ghideon said:

Or in other words: using time t’ from the primed coordinates to calculate a distance  x in the unprimed coordinate system assumes Newtonian physics and Galilean transformations. 

Once again: we talk about the pictures Fig. 4-06 and 4-07 (or Fig. 4-06b and 4-07b, in these are also S depicted).
Can you be more specific and write what are the errors I do? What is incompatible with the first postulate?

[swansont]

1 hour ago, Jan Slowak said:

If you mean your question At the same time in whose frame? then my answer is as follows: in S, this should be obvious.
I write in my explanation of the picture Fig. 4-05: At the same time, an event, a light signal, occurs in the point P_x.
P_x is in the reference system S (x refers to S, x' refers to S').

As I've explained, it's not obvious, because you have intermixed the primed and unprimed. And in fig 4-05, you are describing things in the primed frame. So it is not at all obvious what you are describing.

 

 

[Bufofrog]

2 hours ago, Jan Slowak said:

Can you be more specific and write what are the errors I do? 

Here is a link to a lecture from Yale that clearly explains LT using the same method that you are discussing.  I think it is a quite good lecture.

LINK

[Ghideon]

2 hours ago, Jan Slowak said:

Once again: we talk about the pictures Fig. 4-06 and 4-07 (or Fig. 4-06b and 4-07b, in these are also S depicted).
Can you be more specific and write what are the errors I do? What is incompatible with the first postulate?

If your proposed equation x = vt'+ ct'  where true photons would have a velocity that is frame dependent. For instance would light travel at velocity c in vacuum in one frame of reference and velocity less than c in vacuum in another frame of reference.

your pictures are deliberatly or unintentionally ambigous so that they can’t be used to give any more details that @swansont have given; frames of reference are messad up. We need better pictures and more care about frames of reference. I know how to draw such diagrams. But:

On 6/20/2019 at 4:50 PM, Jan Slowak said:

Please, do not send other pictures.

So you go ahead and draw and I’ll keep pointing out the errors.